Triple differential cross sections d3 sigma /dp3 for charged pions produced in symmetric heavy-ion collisions were measured with the KaoS magnetic spectrometer at the heavy-ion synchrotron facility SIS at GSI. The correlations between the momentum vectors of charged pions and the reaction plane in 197Au+197Au collisions at an incident energy of 1 GeV/nucleon were determined. We observe, for the first time, an azimuthally anisotropic distribution of pions, with enhanced emission perpendicular to the reaction plane. The anisotropy is most pronounced for pions of high transverse momentum in semicentral collisions.